DEPENDENCE OF STABILITY OF NICHOLSON'S BLOWFLIES EQUATION WITH MATURATION STAGE ON PARAMETERS | Zendy

Jianquan Li | Zendy; BaoLin Zhang | Zendy; Yiqun Li | Zendy

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DEPENDENCE OF STABILITY OF NICHOLSON'S BLOWFLIES EQUATION WITH MATURATION STAGE ON PARAMETERS

Author(s) -

Jianquan Li,

BaoLin Zhang,

Yiqun Li

Publication year - 2017

Publication title -

journal of applied analysis and computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.55

H-Index - 21

eISSN - 2158-5644

pISSN - 2156-907X

DOI - 10.11948/2017042

Subject(s) - mathematics , stability (learning theory) , eigenvalues and eigenvectors , characteristic equation , population , mathematical analysis , differential equation , physics , computer science , demography , quantum mechanics , machine learning , sociology

The stability of Nicholson’s blowflies equation with maturation stage is investigated by reducing the number of parameters in the original model. We derive the condition on the stability of the positive equilibrium of the model, and discuss the dependence of the stability on the parameters by analyzing geometrically the dependence of real parts of eigenvalues of the characteristic equation with fewer parameters on the parameters. By restoring parameters, the condition on the stability of the positive equilibrium of the original model are formulated explicitly, and the corresponding regions are depicted for some different cases. The obtained result shows that the parameter determining the maximum reproductive success of the population affects only the size of the positive equilibrium, but plays no role in determining its stability.

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